Simplify. Remove all perfect squares from inside the square root. Assume $a$ is positive. $\sqrt{108a^6}=$
Answer: Factor $108$ and find the greatest perfect square: $108=2\cdot 2\cdot 3\cdot 3\cdot 3=6^2\cdot 3$ Find the greatest perfect square in $a^6$ : $a^6=\left(a^3\right)^2$ $\begin{aligned} \sqrt{108a^6}&=\sqrt{6^2\cdot 3\cdot \left(a^3\right)^2} \\\\ &=\sqrt{6^2}\cdot \sqrt{3} \cdot \sqrt{\left(a^3\right)^2} \\\\ &=6\cdot \sqrt{3} \cdot a^3 \\\\ &=6a^3\sqrt{3} \end{aligned}$